Hidden Variables and the Two Theorems of John Bell

Hidden Variables and the Two Theorems of John Bell

1993 | N. David Mermin
N. David Mermin's article discusses the two key no-hidden-variables theorems by John Bell: the Bell-Kochen-Specker (KS) theorem and Bell's theorem. The KS theorem, less known than Bell's theorem, shows that quantum mechanics cannot be explained by non-contextual hidden-variables theories. Bell's theorem, on the other hand, demonstrates that quantum mechanics is incompatible with local hidden-variables theories. Mermin highlights that the KS theorem can be simplified and made more accessible, and that a new version of the KS theorem can be converted into a form of Bell's theorem, clarifying their conceptual connection. The article begins by explaining the concept of hidden variables and the challenges they pose to quantum mechanics. It then outlines the assumptions of hidden-variables theories and critiques von Neumann's flawed assumption that led to incorrect conclusions. Mermin discusses the Bell-KS theorem, which shows that quantum mechanics cannot be explained by non-contextual hidden-variables theories, and a simpler version of this theorem in 4 dimensions. He also presents a more versatile version in 8 dimensions, which can be converted into a form of Bell's theorem. Mermin addresses the issue of non-contextuality, a key assumption in hidden-variables theories, and argues that it is not as silly as von Neumann's assumption. He explains that non-contextuality is an important constraint in hidden-variables theories and that its incompatibility with quantum mechanics is a fundamental result. The article also discusses the relationship between non-contextuality and locality, showing that Bell's theorem can be derived from the assumption of locality rather than non-contextuality. Mermin concludes by emphasizing the importance of these theorems in understanding the nature of quantum mechanics and the limitations of hidden-variables theories. He also notes that the 8-dimensional version of the Bell-KS theorem provides a conceptual link between the two theorems of John Bell, clarifying their relationship and the implications of each for the interpretation of quantum mechanics.N. David Mermin's article discusses the two key no-hidden-variables theorems by John Bell: the Bell-Kochen-Specker (KS) theorem and Bell's theorem. The KS theorem, less known than Bell's theorem, shows that quantum mechanics cannot be explained by non-contextual hidden-variables theories. Bell's theorem, on the other hand, demonstrates that quantum mechanics is incompatible with local hidden-variables theories. Mermin highlights that the KS theorem can be simplified and made more accessible, and that a new version of the KS theorem can be converted into a form of Bell's theorem, clarifying their conceptual connection. The article begins by explaining the concept of hidden variables and the challenges they pose to quantum mechanics. It then outlines the assumptions of hidden-variables theories and critiques von Neumann's flawed assumption that led to incorrect conclusions. Mermin discusses the Bell-KS theorem, which shows that quantum mechanics cannot be explained by non-contextual hidden-variables theories, and a simpler version of this theorem in 4 dimensions. He also presents a more versatile version in 8 dimensions, which can be converted into a form of Bell's theorem. Mermin addresses the issue of non-contextuality, a key assumption in hidden-variables theories, and argues that it is not as silly as von Neumann's assumption. He explains that non-contextuality is an important constraint in hidden-variables theories and that its incompatibility with quantum mechanics is a fundamental result. The article also discusses the relationship between non-contextuality and locality, showing that Bell's theorem can be derived from the assumption of locality rather than non-contextuality. Mermin concludes by emphasizing the importance of these theorems in understanding the nature of quantum mechanics and the limitations of hidden-variables theories. He also notes that the 8-dimensional version of the Bell-KS theorem provides a conceptual link between the two theorems of John Bell, clarifying their relationship and the implications of each for the interpretation of quantum mechanics.
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